INTEGRATED ALGEBRA
The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
Integrated Algebra
Thursday, January 29, 2009 – 1:15 to 4:15 p.m., only
Print Your Name:
Print Your School’s Name:
Print your name and the name of your school in the boxes above. Then turn to the
last page of this booklet, which is the answer sheet for Part I. Fold the last page along the
perforations and, slowly and carefully, tear off the answer sheet. Then fill in the heading of
your answer sheet.
Scrap paper is not permitted for any part of this examination, but you may use the blank
spaces in this booklet as scrap paper. A perforated sheet of scrap graph paper is provided
at the end of this booklet for any question for which graphing may be helpful but is not
required. You may remove this sheet from this booklet. Any work done on this sheet of
scrap graph paper will not be scored. All work should be written in pen, except graphs and
drawings, which should be done in pencil.
The formulas that you may need to answer some questions in this examination are found
at the end of the examination. This sheet is perforated so you may remove it from this
booklet.
This examination has four parts, with a total of 39 questions. You must answer all
questions in this examination. Write your answers to the Part I multiple-choice questions
on the separate answer sheet. Write your answers to the questions in Parts II, III, and IV
directly in this booklet. Clearly indicate the necessary steps, including appropriate formula
substitutions, diagrams, graphs, charts, etc.
When you have completed the examination, you must sign the statement printed at the
end of the answer sheet, indicating that you had no unlawful knowledge of the questions or
answers prior to the examination and that you have neither given nor received assistance
in answering any of the questions during the examination. Your answer sheet cannot be
accepted if you fail to sign this declaration.
Notice…
A graphing calculator and a straightedge (ruler) must be available for you to use while
taking this examination.
The use of any communications device is strictly prohibited when taking this examination.
If you use any communications device, no matter how briefly, your examination will be
invalidated and no score will be calculated for you.
DO NOT OPEN THIS EXAMINATION BOOKLET UNTIL THE SIGNAL IS GIVEN.
INTEGRATED ALGEBRA
Part I
Answer all questions in this part. Each correct answer will receive 2 credits. No partial credit
will be allowed. For each question, write on the separate answer sheet the numeral preceding
the word or expression that best completes the statement or answers the question. [60]
1 On a certain day in Toronto, Canada, the temperature was
9
15° Celsius (C). Using the formula F = C + 32 , Peter converts
5
this temperature to degrees Fahrenheit (F). Which temperature
represents 15°C in degrees Fahrenheit?
(1) –9
(3) 59
(2) 35
(4) 85
2 What is the speed, in meters per second, of a paper airplane that flies
24 meters in 6 seconds?
(1) 144
(3) 18
(2) 30
(4) 4
3 The faces of a cube are numbered from 1 to 6. If the cube is rolled
once, which outcome is least likely to occur?
(1) rolling an odd number
(2) rolling an even number
(3) rolling a number less than 6
(4) rolling a number greater than 4
Integrated Algebra – Jan. ’09
[]
Use this space for
computations.
4 Tamara has a cell phone plan that charges $0.07 per minute plus a
monthly fee of $19.00. She budgets $29.50 per month for total cell
phone expenses without taxes. What is the maximum number of
minutes Tamara could use her phone each month in order to stay
within her budget?
(1) 150
(3) 421
(2) 271
(4) 692
Use this space for
computations.
0
Temperature
1
2
3
4
5
6
200
180
160
140
120
100
80
60
40
20
0
1
2
3
4
5
Time (minutes)
Time (minutes)
(1)
(3)
Temperature
200
180
160
140
120
100
80
60
40
20
0
(degrees Fahrenheit)
200
180
160
140
120
100
80
60
40
20
1
2
3
4
5
6
(degrees Fahrenheit)
Temperature
Temperature
(degrees Fahrenheit)
(degrees Fahrenheit)
5 Antwaan leaves a cup of hot chocolate on the counter in his kitchen.
Which graph is the best representation of the change in temperature
of his hot chocolate over time?
200
180
160
140
120
100
80
60
40
20
0
1
2
3
4
5
Time (minutes)
Time (minutes)
(2)
(4)
6 What is the solution of
6
k+4
k+9
=
2
3 ?
(1) 1
(3) 6
(2) 5
(4) 14
Integrated Algebra – Jan. ’09
6
[]
[OVER]
7 Alex earned scores of 60, 74, 82, 87, 87, and 94 on his first six algebra
tests. What is the relationship between the measures of central
tendency of these scores?
(1) median < mode < mean
(3) mode < median < mean
(2) mean < mode < median
(4) mean < median < mode
8 The New York Volleyball Association invited 64 teams to compete in
a tournament. After each round, half of the teams were eliminated.
Which equation represents the number of teams, t, that remained in
the tournament after r rounds?
(1) t = 64(r)0.5
(3) t = 64(1.5)r
(2) t = 64(– 0.5)r
(4) t = 64(0.5)r
9 The expression 9x2 – 100 is equivalent to
(1) (9x – 10)(x + 10)
(3) (3x – 100)(3x – 1)
(2) (3x – 10)(3x + 10)
(4) (9x – 100)(x + 1)
10 What is an equation of the line that passes through the points
(3,–3) and (–3,–3)?
(1) y = 3
(3) y = –3
(2) x = –3
(4) x = y
Integrated Algebra – Jan. ’09
[]
Use this space for
computations.
11 If the formula for the perimeter of a rectangle is P = 2l + 2w,
then w can be expressed as
2l –- P
2 P –- 2l
(2) w = 2 Use this space for
computations.
P –- l
2
P –- 2w
(4) w =
2l
(1) w =
(3) w =
12 In the right triangle shown in the diagram below, what is the value of
x to the nearest whole number?
x
30°
24
(1) 12
(3) 21
(2) 14
(4) 28
13 What is the slope of the line that passes through the points (2,5) and
(7,3)?
5
8
(1) – 2 (3) 9
2
9
(2) – 5 (4) 8
Integrated Algebra – Jan. ’09
[]
[OVER]
Use this space for
computations.
2
14 What are the roots of the equation x – 10x + 21 = 0?
(1) 1 and 21
(3) 3 and 7
(2) –5 and –5
(4) –3 and –7
15 Rhonda has $1.35 in nickels and dimes in her pocket. If she has
six more dimes than nickels, which equation can be used to
determine x, the number of nickels she has?
(1) 0.05(x + 6) + 0.10x = 1.35
(2) 0.05x + 0.10(x + 6) = 1.35
(3) 0.05 + 0.10(6x) = 1.35
(4) 0.15(x + 6) = 1.35
16 Which equation represents the axis of symmetry of the graph of the
parabola below?
y
25
–5
x
5
–25
(1) y = –3
(3) y = –25
(2) x = –3
(4) x = –25
Integrated Algebra – Jan. ’09
[]
17��������
The set "1,2,3,4 , is equivalent to
(1) # x ; 1 1 x 1 4,where x is a whole number (2) # x ; 0 1 x 1 4,where x is a whole number (3) # x ; 0 1 x # 4,where x is a whole number (4) # x ; 1 1 x # 4,where x is a whole number -
Use this space for
computations.
2–
26
18 What is the value of x in the equation x 3= x ?
1
(1) – 8
(3) 8
1
(2) – 8 (4) 8
19 The diagram below shows right triangle UPC.
U
8
C
17
15
P
Which ratio represents the sine of ∠U?
15
8
(1) 8 (3)
15
15
8
(2)
(4)
17
17
Integrated Algebra – Jan. ’09
[]
[OVER]
20 What is
72 expressed in simplest radical form?
(1) 2 18 (3) 6 2
(2) 3 8 (4) 8 3
6
2
21 What is 5x –- 3x in simplest form?
8
(1)
(3)
15x 2
8
(2)
(4)
15x
4
15x
4
2x
22 Which ordered pair is a solution of the system of equations
y = x2 – x – 20 and y = 3x – 15?
(1) (–5,–30)
(3) (0,5)
(2) (–1,–18)
(4) (5,–1)
23 A survey is being conducted to determine which types of television
programs people watch. Which survey and location combination
would likely contain the most bias?
(1) surveying 10 people who work in a sporting goods store
(2) surveying the first 25 people who enter a grocery store
(3) randomly surveying 50 people during the day in a mall
(4) randomly surveying 75 people during the day in a clothing store
Integrated Algebra – Jan. ’09
[]
Use this space for
computations.
24 The length of a rectangular room is 7 less than three times the width,
w, of the room. Which expression represents the area of the room?
(1) 3w – 4
(3) 3w2 – 4w
(2) 3w – 7
(4) 3w2 – 7w
25 The function y =
(1) 0 or 3
x
is undefined when the value of x is
–9
x (3) 3, only
(2) 3 or –3
(4) –3, only
Use this space for
computations.
2
26 Which equation represents a line that is parallel to the line
y = 3 – 2x?
(1) 4x + 2y = 5
(3) y = 3 – 4x
(2) 2x + 4y = 1
(4) y = 4x – 2
Integrated Algebra – Jan. ’09
[]
[OVER]
27 What is the product of 8.4 × 108 and 4.2 × 103 written in scientific
notation?
(1) 2.0 × 105 (3) 35.28 × 1011
(2) 12.6 × 1011
(4) 3.528 × 1012
28 Keisha is playing a game using a wheel divided into eight equal
sectors, as shown in the diagram below. Each time the spinner lands
on orange, she will win a prize.
Brown
White
Green
Orange
Yellow
Brown
Brown White
If Keisha spins this wheel twice, what is the probability she will win a
prize on both spins?
1
(1) 64 1
(2)
56
Integrated Algebra – Jan. ’09
1
(3) 16
1
(4) 4
[10]
Use this space for
computations.
29 A movie theater recorded the number of tickets sold daily for a
popular movie during the month of June. The box-and-whisker plot
shown below represents the data for the number of tickets sold, in
hundreds.
0
1
2
3
4
5
6
7
8
9
Use this space for
computations.
10
Which conclusion can be made using this plot?
(1) The second quartile is 600.
(2) The mean of the attendance is 400.
(3) The range of the attendance is 300 to 600.
(4) Twenty-five percent of the attendance is between 300 and 400.
30 Which graph represents a function?
y
y
x
x
(1)
(3)
y
y
x
x
(2)
Integrated Algebra – Jan. ’09
(4)
[11]
[OVER]
Part II
Answer all questions in this part. Each correct answer will receive 2 credits. Clearly indicate
the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.
For all questions in this part, a correct numerical answer with no work shown will receive only
1 credit. [6]
31 A window is made up of a single piece of glass in the shape of a semicircle and a rectangle, as
shown in the diagram below. Tess is decorating for a party and wants to put a string of lights all the
way around the outside edge of the window.
Window
12 ft
10 ft
To the nearest foot, what is the length of the string of lights that Tess will need to decorate
the window?
Integrated Algebra – Jan. ’09
[12]
32 Simplify:
27k 5 m8
^ 4k 3 h ^ 9m 2 h
Integrated Algebra – Jan. ’09
[13]
[OVER]
33 The table below represents the number of hours a student worked and the amount of money the
student earned.
Number
of Hours
(h)
Dollars
Earned
(d)
8
$50.00
15
$93.75
19
$118.75
30
$187.50
Write an equation that represents the number of dollars, d, earned in terms of the number of
hours, h, worked.
Using this equation, determine the number of dollars the student would earn for working
40 hours.
Integrated Algebra – Jan. ’09
[14]
Part III
Answer all questions in this part. Each correct answer will receive 3 credits. Clearly indicate
the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.
For all questions in this part, a correct numerical answer with no work shown will receive only
1 credit. [9]
34 Sarah measures her rectangular bedroom window for a new shade. Her measurements are
36 inches by 42 inches. The actual measurements of the window are 36.5 inches and 42.5 inches.
Using the measurements that Sarah took, determine the number of square inches in the area of
the window.
Determine the number of square inches in the actual area of the window.
Determine the relative error in calculating the area. Express your answer as a decimal to the
nearest thousandth.
Integrated Algebra – Jan. ’09
[15]
[OVER]
35 Perform the indicated operation and simplify:
Integrated Algebra – Jan. ’09
3x + 6
x 2 -– 4
'
x+3
4x + 12
[16]
36 A soup can is in the shape of a cylinder. The can has a volume of 342 cm3 and a diameter of 6 cm.
Express the height of the can in terms of π.
Determine the maximum number of soup cans that can be stacked on their base between
two shelves if the distance between the shelves is exactly 36 cm. Explain your answer.
Integrated Algebra – Jan. ’09
[17]
[OVER]
Part IV
Answer all questions in this part. Each correct answer will receive 4 credits. Clearly indicate
the necessary steps, including appropriate formula substitutions, diagrams, graphs, charts, etc.
For all questions in this part, a correct numerical answer with no work shown will receive only
1 credit. [12]
37 Solve the following system of equations algebraically:
3x + 2y = 4
4x + 3y = 7
[Only an algebraic solution can receive full credit.]
Integrated Algebra – Jan. ’09
[18]
38 On the set of axes below, graph the following system of inequalities and state the coordinates of a
point in the solution set.
2x -– y $ 6
x22
y
x
Integrated Algebra – Jan. ’09
[19]
[OVER]
39 A restaurant sells kids’ meals consisting of one main course, one side dish, and one drink, as shown
in the table below.
Kids’ Meal Choices
Main Course
Side Dish
Drink
hamburger
French fries
milk
chicken nuggets
applesauce
juice
turkey sandwich
soda
Draw a tree diagram or list the sample space showing all possible kids’ meals. How many different
kids’ meals can a person order?
José does not drink juice. Determine the number of different kids’ meals that do not include
juice.
José’s sister will eat only chicken nuggets for her main course. Determine the number of different
kids’ meals that include chicken nuggets.
Integrated Algebra – Jan. ’09
[20]
Tear Here
Reference Sheet
Trigonometric Ratios
sin A =
opposite
hypotenuse
cos A =
adjacent
hypotenuse
tan A =
opposite
adjacent
Area
trapezoid
Volume
cylinder
A = –12 h(b1 + b2)
V = πr2h
rectangular prism
SA = 2lw + 2hw + 2lh
Surface Area
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cylinder
Coordinate Geometry
Integrated Algebra – Jan. ’09
SA = 2πr2 + 2πrh
𝚫y y – y
m = 𝚫 x = x2 – x 1
2
1
[23]
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Integrated Algebra – Jan. ’09
[24]
Tear Here
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Scrap Graph Paper — This sheet will not be scored.
Scrap Graph Paper — This sheet will not be scored.
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The University of the State of New York
REGENTS HIGH SCHOOL EXAMINATION
Tear Here
INTEGRATED ALGEBRA
Thursday, January 29, 2009 – 1:15 to 4:15 p.m., only
ANSWER SHEET
Student . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sex: ❑Male
❑Female
Grade . . . . . . . . Teacher . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . School . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Your answers to Part I should be recorded on this answer sheet.
Part I
Answer all 30 questions in this part.
1 . . . . . . . . . . . . . . . 9 . . . . . . . . . . . . . . . 17 . . . . . . . . . . . . . . . 25 . . . . . . . . . . . . . . . 2 . . . . . . . . . . . . . . . 10 . . . . . . . . . . . . . . . 18 . . . . . . . . . . . . . . . 26 . . . . . . . . . . . . . . . 3 . . . . . . . . . . . . . . . 11 . . . . . . . . . . . . . . . 19 . . . . . . . . . . . . . . . 27 . . . . . . . . . . . . . . . 4 . . . . . . . . . . . . . . . 12 . . . . . . . . . . . . . . . 20 . . . . . . . . . . . . . . . 28 . . . . . . . . . . . . . . . 5 . . . . . . . . . . . . . . . 13 . . . . . . . . . . . . . . . 21 . . . . . . . . . . . . . . . 29 . . . . . . . . . . . . . . . 6 . . . . . . . . . . . . . . . 14 . . . . . . . . . . . . . . . 22 . . . . . . . . . . . . . . . 30 . . . . . . . . . . . . . . . 7 . . . . . . . . . . . . . . . 15 . . . . . . . . . . . . . . . 23 . . . . . . . . . . . . . . . 8 . . . . . . . . . . . . . . . 16 . . . . . . . . . . . . . . . 24 . . . . . . . . . . . . . . . Your answers for Parts II, III, and IV should be written in the test booklet.
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The declaration below should be signed when you have completed the examination.
I do hereby affirm, at the close of this examination, that I had no unlawful knowledge of the questions or answers
prior to the examination and that I have neither given nor received assistance in answering any of the questions during the
examination.
Integrated Algebra – Jan. ’09
Signature
[27]
INTEGRATED ALGEBRA
Rater’s/Scorer’s Name
(minimum of three)
INTEGRATED ALGEBRA
Maximum
Credit
Part I 1–30
60
Part II
31
2
32
2
33
2
Part III
34
3
35
3
36
3
Part IV 37
4
38
4
39
4
Maximum
Total
87
Credits
Earned
Rater’s/Scorer’s
Initials
Total Raw
Score
Checked by
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Question
Scaled Score
(from conversion chart)
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[28]
INTEGRATED ALGEBRA
Integrated Algebra – Jan. ’09